Jeffrey Weeks (mathematician)
Encyclopedia
Jeffrey Renwick Weeks is an American
mathematician
, a geometric topologist
and cosmologist.
from Dartmouth College
in 1978, and his Ph.D.
in mathematics
from Princeton University
in 1985, under the supervision of William Thurston
. Since then he has taught at Stockton State College, Ithaca College
, and Middlebury College
, but has spent much of his time as a free-lance mathematician.
s and physical cosmology
.
The Weeks manifold
, discovered in 1985 by Weeks, is the hyperbolic 3-manifold
with the minimum possible volume. Weeks has written various computer programs to assist in mathematical research and mathematical visualization
. His SnapPea
program is used to study hyperbolic 3-manifold
s, while he has also developed interactive software to introduce these ideas to middle-school, high-school, and college students.
Weeks is particularly interested in using topology
to understand the spatial universe. His book The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds (Marcel Dekker, 1985, ISBN 0-8247-7437-X) explores the geometry and topology of low-dimensional manifold
s. The second edition (2002, ISBN 0-8247-0709-5) explains some of his work in applying the material to cosmology.
in 1999. In 2007, he won the Levi L. Conant
Prize for his expository paper, "The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations" (Notices of the AMS 2004), and in 2008 he gave the first Levi Conant Lecture at Conant's former employer, the Worcester Polytechnic Institute
.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, a geometric topologist
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
and cosmologist.
Biography
Weeks received his B.A.Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
from Dartmouth College
Dartmouth College
Dartmouth College is a private, Ivy League university in Hanover, New Hampshire, United States. The institution comprises a liberal arts college, Dartmouth Medical School, Thayer School of Engineering, and the Tuck School of Business, as well as 19 graduate programs in the arts and sciences...
in 1978, and his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1985, under the supervision of William Thurston
William Thurston
William Paul Thurston is an American mathematician. He is a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds...
. Since then he has taught at Stockton State College, Ithaca College
Ithaca College
Ithaca College is a private college located on the South Hill of Ithaca, New York. The school was founded by William Egbert in 1892 as a conservatory of music. The college has a strong liberal arts core, but also offers several pre-professional programs and some graduate programs. The college is...
, and Middlebury College
Middlebury College
Middlebury College is a private liberal arts college located in Middlebury, Vermont, USA. Founded in 1800, it is one of the oldest liberal arts colleges in the United States. Drawing 2,400 undergraduates from all 50 United States and over 70 countries, Middlebury offers 44 majors in the arts,...
, but has spent much of his time as a free-lance mathematician.
Research
Weeks' research contributions have mainly been in the field of 3-manifold3-manifold
In mathematics, a 3-manifold is a 3-dimensional manifold. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.Phenomena in three dimensions...
s and physical cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...
.
The Weeks manifold
Weeks manifold
In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by and Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.9427... and showed that it has the smallest volume of any closed orientable...
, discovered in 1985 by Weeks, is the hyperbolic 3-manifold
Hyperbolic 3-manifold
A hyperbolic 3-manifold is a 3-manifold equipped with a complete Riemannian metric of constant sectional curvature -1. In other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously...
with the minimum possible volume. Weeks has written various computer programs to assist in mathematical research and mathematical visualization
Mathematical visualization
Mathematical visualization is an aspect of geometry which allows one to understand and explore mathematical phenomena via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models , while today it most frequently consists of using computers to make...
. His SnapPea
SnapPea
SnapPea is free software designed to help mathematicians, in particular low-dimensional topologists, study hyperbolic 3-manifolds. The primary developer is Jeffrey Weeks, who created the first version as part of his doctoral thesis, supervised by William Thurston. The latest version is 3.0d3...
program is used to study hyperbolic 3-manifold
Hyperbolic 3-manifold
A hyperbolic 3-manifold is a 3-manifold equipped with a complete Riemannian metric of constant sectional curvature -1. In other words, it is the quotient of three-dimensional hyperbolic space by a subgroup of hyperbolic isometries acting freely and properly discontinuously...
s, while he has also developed interactive software to introduce these ideas to middle-school, high-school, and college students.
Weeks is particularly interested in using topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
to understand the spatial universe. His book The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds (Marcel Dekker, 1985, ISBN 0-8247-7437-X) explores the geometry and topology of low-dimensional manifold
Manifold
In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....
s. The second edition (2002, ISBN 0-8247-0709-5) explains some of his work in applying the material to cosmology.
Awards and honors
Weeks became a MacArthur FellowMacArthur Foundation
The John D. and Catherine T. MacArthur Foundation is one of the largest private foundations in the United States. Based in Chicago but supporting non-profit organizations that work in 60 countries, MacArthur has awarded more than US$4 billion since its inception in 1978...
in 1999. In 2007, he won the Levi L. Conant
Levi L. Conant
Levi Leonard Conant was an American mathematician specializing in trigonometry.-Education and career:...
Prize for his expository paper, "The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations" (Notices of the AMS 2004), and in 2008 he gave the first Levi Conant Lecture at Conant's former employer, the Worcester Polytechnic Institute
Worcester Polytechnic Institute
Worcester Polytechnic Institute is a private university located in Worcester, Massachusetts, in the United States.Founded in 1865 in Worcester, WPI was one of the United States' first engineering and technology universities...
.